Sloution to problem set 7

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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1. We use a Normal approximation to the Binomial distribution: X b(x;1000,.03) N(30,5.394) a. () () = = 394 . 5 30 5 . 39 1 39 1 40 Z P x P x P 0392 . 9608 . 1 ) 76 . 1 ( 1 = = Φ = b. 5% of 1000 = 50: () 00 . 1 ) 80 . 3 ( 394 . 5 30 5 . 50 50 Φ = = Z P x P 2. P: .5 .6 .8 µ : 12.5 15 20 σ : 2.50 2.45 2.00 a. P(15 X 20) P(14.5 normal 20.5) .5 .212 P(.80 Z 3.20) = .2112 .6 .577 P(-.20 Z 2.24) = .5668 .8 .573 P(-2.75 Z .25) = .5957 b. c. 3. P = .10; n = 200; np = 20, npq = 18 a. P(X 30) = + Φ 18 20 5 . 30 = Φ (2.47) = .9932 b. P(X < 30) =P(X 29) = + Φ 18 20 5 . 29 = Φ (2.24) = .9875 P(X 15) P(normal 15.5) .885 P(Z 1.20) = .8849 .575 P(Z .20) = .5793 .017 P( Z -2.25) = .0122 P(20 X) P(19.5 normal) .002 .0026 .029 .0329 .617 .5987
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c. P(15
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Sloution to problem set 7 - 1. We use a Normal...

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